Identifying learning obstacles in proof construction for geometric transformations: Conceptual, procedural, and visualization errors

Abstract

This study investigates learning obstacles encountered by pre-service mathematics teachers in constructing proofs for geometric transformations, a topic that has not been extensively examined in previous research. In contrast to prior studies, this research identifies specific types of errors, as well as their interconnections, representing the first step in uncovering learning obstacles. The study followed the four steps of phenomenology: bracketing, intuiting, analyzing, and describing, using written tests and interviews to explore students' errors. The findings reveal that errors can be categorized into three types: visualization errors, conceptual errors, and procedural errors. The analysis of their interconnections revealed that conceptual errors were the primary factor contributing to both procedural and visualization errors. Analyzing these errors led to the identification of epistemological obstacles, which manifested when participants struggled to apply fundamental concepts—such as injectivity, surjectivity, and bijectivity—to more complex tasks. Therefore, the study concludes that the primary learning obstacle discovered is an epistemological obstacle.